After lots of reading, it seems it is possible (thanks for the link, OGELTHORPE), but I haven't been able to figure out the right cable configuration.
Confirmed my MacBook Pro (mid 2012) supports two Thunderbolt Displays
Confirmed my iMac (mid 2010) supports Target Display Mode
Confirmed this is possible based on the below...
Yes. If your Thunderbolt-equipped Mac supports two Thunderbolt displays this is possible. Your Thunderbolt-equipped Mac will need to be connected to your Apple Thunderbolt display and the iMac will need to be connected to the Thunderbolt port of the Apple Thunderbolt display. Not all iMacs support Target Display Mode. See Target Display Mode: Frequently Asked Questions (FAQ) for more information. Once connected, place the iMac into Target Display Mode to enable it as the second external display.
Notes:
- Make sure the Thunderbolt Display is connected to your Thunderbolt-equipped Mac and is being recognized and used by the Thunderbolt-equipped Mac before connecting the iMac to the Thunderbolt display.
- If the iMac is placed in the Thunderbolt chain before the Apple Thunderbolt Display, the Thunderbolt display will work as an external display for the iMac and it will stay active as an external display for the iMac, but it will not function with the main Thunderbolt-equipped Mac using the iMac's display.
- To use an iMac in Target Display Mode when connected to an Apple Thunderbolt Display, the iMac must be Thunderbolt-enabled, and a Thunderbolt cable must be used (not a mini-DP cable).
The bulletpoint that worries me is the last one. I have tried with both a mini display port cable AND a thunderbolt cable, but the last bulletpoint seems to suggest that this is not possible if the iMac is NOT a Thunderbolt enabled iMac (which mine isn't). It does however say elsewhere that my iMac acting in TDM mode acts as a Thunderbolt Display, so it's all a bit confusing!!! It seems that my MacBook Pro can't drive both displays; so now I'm trying to figure out how to get the iMac to treat my Thunderbolt display as a second monitor.
Fingers crossed...